Questions: Transform each graph as specified below. (a) The graph of y=f(x) is shown. Draw the graph of y=2 f(x).

Transcript text: Transform each graph as specified below. (a) The graph of $y=f(x)$ is shown. Draw the graph of $y=2 f(x)$.

Solution

Solution Steps

Step 1: Identify the key points of the original graph

The graph of $y = f(x)$ is a V-shaped graph with the vertex at (0, 0). Two other points on the graph are (-2, 4) and (2, 4).

Step 2: Apply the transformation

The transformation $y = 2f(x)$ represents a vertical stretch by a factor of 2. This means that the y-coordinates of all points on the graph are multiplied by 2, while the x-coordinates remain unchanged.

Step 3: Calculate the new coordinates

The vertex (0, 0) remains at (0, 0) since $2 * 0 = 0$. The point (-2, 4) transforms to (-2, 8) since $2 * 4 = 8$. The point (2, 4) transforms to (2, 8) since $2 * 4 = 8$.

Step 4: Draw the transformed graph

The transformed graph will still be V-shaped, with the vertex at (0, 0). The graph will pass through the points (-2, 8) and (2, 8). The graph is stretched vertically by a factor of 2.